Research of Neural Network Classifier Based on FCM and PSO for Breast Cancer Classification

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1 Research of Neural Network Classfer Based on FCM and PSO for Breast Cancer Classfcaton Le Zhang 1, Ln Wang 1, Xujewen Wang 2, Keke Lu 2, and Ajth Abraham 3 1 Shandong Provncal Key Laboratory of Network Based Intellgent Computng, Unversty of Jnan, Jnan, Chna {Zhangle,se_wangln}@ujn.edu.cn 2 Unversty of Jnan, Jnan, Chna kevnxw@foxmal.com,dp_lukk@ujn.edu.cn 3 Machne Intellgence Research Labs (MIR Labs), USA ajth.abraham@eee.org Abstract. Breast cancer s one of the most common tumors related to death n women n many countres. In ths paper, a novel neural network classfcaton model s developed. The proposed model uses floatng centrods method and partcle swarm optmzaton algorthm wth nerta weght as optmzer to mprove the performance of neural network classfer. Wsconsn breast cancer datasets n UCI Machne Learnng Repostory are tested wth neural network classfer of the proposed method. Expermental results show that the developed model mproves search convergence and performance. The accuracy of classfcaton of bengn and malgnant tumors could be mproved by the developed method compared wth other classfcaton technques. Keywords: Floatng Centrods Method, PSO, Neural Network, Breast Cancer Classfcaton. 1 Introducton Breast cancer s one of the most common malgnant tumors among women. Varous artfcal ntellgence technques [1-6] have been used to mprove the accuracy and effcency of cancer dagnoss. In recent years, neural network has wdely been appled to feature extracton, data compresson, data classfcaton, clusterng etc. [7]. The learnng algorthm of neural network s a supervsed learnng method. A classfer s usually constructed accordng to the character of a gven datasets and analyzed the character of the gven datasets. It s produced an exact model for each category data. In recent research, many classfcaton technques have been proposed, such as genetc algorthm [8], neural network [9-12], support vector machne [13-16], decson tree [17,18], etc.. Neural network model has been successfully used n many classfcaton problems among these technques. Conductng neural network classfer, the number of parameters ncludng nput layer, hdden layer and output layer s decded by the property, category and characters of dataset. In neural network classfer, sample s mapped by neural network. E. Corchado et al. (Eds.): HAIS 2012, Part I, LNCS 7208, pp , Sprnger-Verlag Berln Hedelberg 2012

2 648 L. Zhang et al. Centrod s a pont n partton space and denotes the center of a class. In a conventonal neural network classfer, poston of centrods and the relatonshp between centrods and classes are set manually. In addton, number of centrods s fxed wth reference to the number of classes. Ths fxed-centrod constrant decreases the chance to fnd optmal neural network. Therefore, a novel neural network classfer based on float centrods method (FCM) whch removes the fxed-centrod constrant and spread the centrods throughout the partton space s proposed n our prevous research [19]. However, despte the superor classfcaton results, the tranng effcency s not acceptable whch lmts the scope of applcaton n practce. Therefore, ths paper presents a developed method adopted partcle swarm optmzaton algorthm wth nerta weght as optmzer to mprove the search convergence and performance of FCM. The rest of the paper s organzed as follows: Secton 2 descrbes the partcle swarm optmzaton algorthm wth nerta weght. Secton 3 provdes the floatng centrods method algorthm and the process of learnng algorthm n detal. Experment results are presented n Secton 4, together wth some comparsons wth other classfcaton technques. In the end, Secton 5 concludes wth a bref summary of our study. 2 Partcle Swarm Optmzaton Algorthm wth Inerta Weght The Partcle Swarm Optmzaton (PSO) algorthm whch s put forward by Kennedy and Eberhart s one of evolutonary algorthms [21]. It s an adaptve method that can be used to solve optmzaton problem. Conductng search uses a populaton of partcle whch corresponds to ndvduals. A populaton of partcles s randomly generated ntally. Each partcle s poston represents a possble soluton pont n the problem space. Each partcle has an updatng poston vector x and updatng velocty vector v by movng through the problem space. At each step, a ftness functon evaluatng each partcle s qualty s calculated by poston vector x. The vector p represents the best ever poston of each partcle and p g represents the best poston obtaned so far n the populaton. For each teraton t, followng the ndvdual best poston p and the global best poston p g, the velocty vector of partcle s updated by: v ( g t t + 1) = v ( t) + c φ ( p ( t) x ( t)) + c φ ( p ( t) x ( )) (1) where c 1 and c 2 are postve constant and φ 1 and φ 2 are unformly dstrbuted random number n [0,1]. The velocty vector v s range of [-V max, V max ]. Updatng the velocty vector of partcle by ths method enables the partcle to search around ts

3 Research of Neural Network Classfer Based on FCM and PSO 649 ndvdual best poston and global best poston. Based on the updated velocty, each partcle changes ts poston accordng to the followng formula: x ( t + 1) = x ( t) + v ( t + 1) (2) Based on ths method, the populaton of partcles tends to cluster together. To avod premature convergence, the followng formula can mprove the velocty vector of each partcle addng the nerta weght factor ω [21]. v ( t + 1) = v ( t) + c1φ1 ( p ( t) x ( t)) + c2φ2 ( pg t ( t) x ( )) ω (3) where nerta weght factor ω s a real number. The nerta weght factor ω controls the magntude of the velocty vector v. The nerta weght factor ω s a rato factor related to the prevous velocty. The nerta weght factor ω decdes the nfluence from the prevous velocty to current velocty. The large nerta weght factor ω can make globally search and the small nerta weght factor ω wll make local search [22]. The fellow method s adopted by the nerta factor ω from ω max toω mn : ω = ( ω ω ) *(maxter ter)/ maxter + ω (4) max mn where maxter s the total number of teraton, ter s the current teraton. Lnearly decreasng the nerta factor ω from ω max to ωmn can mprove the search area frstly and locate the best poston quckly. Wth the nerta weght factor ω gradually decreasng, the velocty of partcle becomes slower and makes local search subtly. The convergence becomes faster owng to add the nerta weght factor. mn 3 The Procedure of Learnng Algorthm for FCM and PSO 3.1 Floatng Centrods Method FCM [19] s an approach whch has some floatng centrods wth class labels spread n the partton space. A sample s labeled by a certan class when the closest centrod of ts correspondng mapped pont s the closest centrods of ths certan class. The partton space s decded by an rregular regons controlled by centrods. To get these floatng centrods, tranng samples are mapped to partton space by neural network, and then, correspondng mapped ponts n partton space wll be parttoned nto several numbers of dsjont subsets usng the K-Means clusterng algorthm [20]. The floatng centrods are defned as computng the cluster centers of these subsets. So, the number of centrods may be more than the number of classes. Fnally, each of these centrods wll be labeled by one class. If tranng ponts of one class are majorty among all the ponts whch belong to a centrod, the centrod s labeled by ths class. More than one centrod can be labeled by one class.

4 650 L. Zhang et al. The floatng centrods method can acheve the optmzaton objectve of neural network classfer, because t s no constrant n the number of centrods and the class label of centrods are computed by the mapped ponts n partton space. The floatng centrods method has no fxed-centrod. The functon of floatng centrods method s that allocates ponts n the same class together as close as possble and separates ponts n the dfferent classes from the partton space. 3.2 Model of Neural Network Classfer A neural network classfer s a par (F, P), where centrod n P have been colored. The model neural network classfer s descrbed by Fg. 1. If a new dataset need to be categorzed, t can be mapped one pont n P used by F, then predct the category accordng to the dstance whch measured by Eucldan dstance. Ths process s llustrated n Fg.2. The dmenson of partton space s set to two and the number of classes s three. Fg. 1. Model of classfer Fg. 2. Categorzng a new sample 3.3 Centrods Generaton Frstly, the tranng dataset s mapped to partton space usng by neural network. The mapped pont correspondng to tranng data s named colored pont. The colored ponts n partton space are dvded nto k dsjont clusters used by K-means algorthm. Then each centrod s labeled category tag accordng to the prncple whch s

5 Research of Neural Network Classfer Based on FCM and PSO 651 that f the color ponts of one class are majorty n all of color ponts, the class should color the centrod. One class can color one or more centrods. If the number of datasets between classes s dfferent, t should keep equtableness usng weghts or other solutons. One class colors a centrod by a hgher probablty, f the number of ths class dataset s larger than others. 3.4 The Process of Learnng Algorthm The goal of learnng algorthm s to get the best neural network and t correspondng colored partton space. The process of learnng algorthm s descrbed by Algorthm 1. Algorthm 1: The process of learnng algorthm Input: User-defned parameters and tranng data set; Output: Best neural network and ts correspondng colored partton space; Step 1: Code neural network to form ndvdual accordng to the partcle swarm optmzaton mentoned wth nerta weght n Secton 2; Step 2: whle maxmum generaton has not been reached do; Step 3: for =1 to the number of ndvduals do; Step 4: Decode ndvdual d to form a neural network; Step 5: Perform centrod generaton wth ths neural network to get colored partton space; Step 6: Use ths neural network and ts correspondng colored partton space to compute the value of optmzaton target functon as the ftness of ndvdual ; Step 7: end for; Step 8: Perform an teraton of mproved partcle swarm optmzaton algorthm, update ndvduals by ther ftness; Step 9: end whle; Step 10: return the best neural network and ts correspondng colored partton space. 3.5 Target Functon The optmzaton target functon s defned as the follow formula, F = s = Z e a (1 2 ) (5) where Z s the value of pont sample whch s mappng to the partton space. S s total number of samples n the tranng dataset and a s a real constant whch controls tortuosty. The target functon s to put ponts n the same class together as close as possble and keep ponts n the dfferent class away from others as far as possble.

6 652 L. Zhang et al. 4 Experments and Results The crteron of testng accuracy s defned to evaluate the performance of ths method. Testng accuracy (TA) whch s a method to obtan better generalzaton capablty s adopted testng data to acheve the accurate rate. TPtest TA = *100% (6) P test where TPtest represent the number of correctly classfed samples n testng dataset and P test s number of total samples n testng dataset. To test the effectveness of the proposed method, we select the Wsconsn breast cancer datasets for the experments whch s selected from the UCI machne learnng database generated by Dr. Wllam from the Unversty of Wsconsn Madson [24]. Breast cancer can be dagnosed bengn or malgnant by puncture samplng. Wsconsn breast cancer dataset conssts of 569 records and 2 classes, whch 357 records are bengn type and 212 records are malgnant type. Each record has 30 attrbutes ncludng ten quantfyng feature, such as dameter, permeter, symmetry etc. The breast cancer datasets s dvded nto two subsets randomly, one s selected as the tranng dataset and the other s the testng dataset. There are 285 records as tranng dataset and 284 records as testng dataset for bengn and malgnant type. Ths two type expermental data have been done respectvely. One class of sample s used for the bengn and the other s used for the malgnant. The normal data s labeled as 1 and the abnormal data s labeled as 0. In our experments, a three-layered feed-forward neural network wth 15 hdden neurons s adopted and the partcle swarm optmzaton algorthm wth nerta weght s selected as optmzer. Ths proposed method s compared wth the other neural network classfers, ncludng Flexble Neural Tree (FNT) [23], Neural Network (NN) and Wavelet Neural Network (WNN) [25]. The parameters of PSO algorthm are mportant factors on searchng the optmal soluton. Through trals on these datasets, the parameters settng of partcle swarm optmzaton algorthm s defned by the follow Table 1. Table 1. Parameters for experments Populaton sze 20 Generaton 3000 W max 0.8 W mx 0.4 C 1 2 C 2 2 V max 3 V mn -3

7 Research of Neural Network Classfer Based on FCM and PSO 653 Table 2 depcts the accuracy results for testng data wth comparson between our method and other methods. The result ndcates that our proposed method s fully capable of mprovng the generalzaton ablty of neural network classfer. Table 2. Testng accuracy (%) Cancer type FNT NN WNN Our method Bengn Malgnant Conclusons In ths paper, a novel neural network s proposed based on floatng centrods method and partcle swarm optmzaton algorthm. Ths approach makes sample to be mapped nto neural network and partton space s used to categorze data sample. The proposed method removes the fxed-centrod constrant. An mproved partcle swarm optmzaton wth nerta weght s adopted as optmzer n ths paper. It ncreases the varety of partcles and mproves the performance and convergence of standard partcle swarm optmzaton algorthm. To evaluate the performance of our proposed approach, Wsconsn breast cancer datasets from UCI machne learnng repostory s selected to compare the accuracy measure wth FNT, NN and WNN. Expermental results llustrate that our method s more effcent than other methods n classfcaton accuracy of breast cancer dataset. Acknowledgements. Ths work was supported by the Natural Scence Foundaton of Shandong Provnce No. ZR2011FL021, the Natural Scence Foundaton of Chna No , the Scence and Technology Development Program of Shandong Provnce No. 2011GGX References 1. Hulka, B.S., Moorman, P.G.: Breast Cancer: Hormones and Other Rsk Factors. Maturtas 38(1), (2001) 2. Corchado, E., Graña, M., Woznak, M.: New trends and applcatons on hybrd artfcal ntellgence systems. Neurocomputng 75(1), (2012) 3. García, S., Fernández, A., Luengo, J., Herrera, F.: Advanced nonparametrc tests for multple comparsons n the desgn of experments n computatonal ntellgence and data mnng: Expermental analyss of power. Informaton Scences 180(10), (2010) 4. Corchado, E., Abraham, A., Carvalho, A.: Hybrd ntellgent algorthms and applcatons. Informaton Scences 180(14), (2010) 5. Pedrycz, W., Alev, R.: Logc-orented neural networks for fuzzy neurocomputng. Neurocomputng 73(1-3), (2009) 6. Abraham, A., Corchado, E., Corchado, J.M.: Hybrd learnng machnes. Neurocomputng 72(13-15), (2009)

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